Tag: Galois-Plane Models

Dodecahedron Model of PG(2,5)

Recent posts tagged Sagan Dodecahedron  mention an association between that Platonic solid and the 5×5 grid. That grid, when extended by the six points on a "line at infinity,"…

Platonic Analogy

(Five by Five continued) As the 3×3 grid underlies the order-3 finite projective plane, whose 13 points may be modeled by the 13 symmetry axes of the cube, so the 5×5…

Pyramid Dance

Oslo artist Josefine Lyche has a new Instagram post, this time on pyramids (the monumental kind). My response — Wikipedia's definition of a tetrahedron as a "triangle-based pyramid" ……

Two Physical Models of the Fano Plane

The Regular Tetrahedron The seven symmetry axes of the regular tetrahedron are of two types: vertex-to-face and edge-to-edge. Take these axes as the "points" of a Fano plane….

A Tetrahedral Fano-Plane Model

Update of Nov. 30, 2014 — It turns out that the following construction appears on pages 16-17 of A Geometrical Picture Book , by  Burkard Polster (Springer, 1998). "Experienced…

Class Act

Update of Nov. 30, 2014 — For further information on the geometry in the remarks by Eberhart below, see pp. 16-17 of A Geometrical Picture Book , by Burkard Polster (Springer,…

Euclidean-Galois Interplay

For previous remarks on this topic, as it relates to symmetry axes of the cube, see previous posts tagged Interplay. The above posts discuss, among other things, the Galois projective…